/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date:        19. March 2015
* $Revision: 	V.1.4.5
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_biquad_cascade_df2T_f64.c
*
* Description:  Processing function for the floating-point transposed
*               direct form II Biquad cascade filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
* @ingroup groupFilters
*/

/**
* @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
*
* This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
* The filters are implemented as a cascade of second order Biquad sections.
* These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
* Only floating-point data is supported.
*
* This function operate on blocks of input and output data and each call to the function
* processes <code>blockSize</code> samples through the filter.
* <code>pSrc</code> points to the array of input data and
* <code>pDst</code> points to the array of output data.
* Both arrays contain <code>blockSize</code> values.
*
* \par Algorithm
* Each Biquad stage implements a second order filter using the difference equation:
* <pre>
*    y[n] = b0 * x[n] + d1
*    d1 = b1 * x[n] + a1 * y[n] + d2
*    d2 = b2 * x[n] + a2 * y[n]
* </pre>
* where d1 and d2 represent the two state values.
*
* \par
* A Biquad filter using a transposed Direct Form II structure is shown below.
* \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
* Pay careful attention to the sign of the feedback coefficients.
* Some design tools flip the sign of the feedback coefficients:
* <pre>
*    y[n] = b0 * x[n] + d1;
*    d1 = b1 * x[n] - a1 * y[n] + d2;
*    d2 = b2 * x[n] - a2 * y[n];
* </pre>
* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
*
* \par
* Higher order filters are realized as a cascade of second order sections.
* <code>numStages</code> refers to the number of second order stages used.
* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the
* coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
*
* \par
* <code>pState</code> points to the state variable array.
* Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
* The state variables are arranged in the <code>pState</code> array as:
* <pre>
*     {d11, d12, d21, d22, ...}
* </pre>
* where <code>d1x</code> refers to the state variables for the first Biquad and
* <code>d2x</code> refers to the state variables for the second Biquad.
* The state array has a total length of <code>2*numStages</code> values.
* The state variables are updated after each block of data is processed; the coefficients are untouched.
*
* \par
* The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
* The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
* That is why the Direct Form I structure supports Q15 and Q31 data types.
* The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.
* Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
* The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
*
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
*
* \par Init Functions
* There is also an associated initialization function.
* The initialization function performs following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
* To do this manually without calling the init function, assign the follow subfields of the instance structure:
* numStages, pCoeffs, pState. Also set all of the values in pState to zero.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* For example, to statically initialize the instance structure use
* <pre>
*     arm_biquad_cascade_df2T_instance_f64 S1 = {numStages, pState, pCoeffs};
* </pre>
* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.
* <code>pCoeffs</code> is the address of the coefficient buffer;
*
*/

/**
* @addtogroup BiquadCascadeDF2T
* @{
*/

/**
* @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
* @param[in]  *S        points to an instance of the filter data structure.
* @param[in]  *pSrc     points to the block of input data.
* @param[out] *pDst     points to the block of output data
* @param[in]  blockSize number of samples to process.
* @return none.
*/


LOW_OPTIMIZATION_ENTER
void arm_biquad_cascade_df2T_f64(
    const arm_biquad_cascade_df2T_instance_f64 *S,
    float64_t *pSrc,
    float64_t *pDst,
    uint32_t blockSize)
{

    float64_t *pIn = pSrc;                         /*  source pointer            */
    float64_t *pOut = pDst;                        /*  destination pointer       */
    float64_t *pState = S->pState;                 /*  State pointer             */
    float64_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
    float64_t acc1;                                /*  accumulator               */
    float64_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
    float64_t Xn1;                                 /*  temporary input           */
    float64_t d1, d2;                              /*  state variables           */
    uint32_t sample, stage = S->numStages;         /*  loop counters             */

#if defined(ARM_MATH_CM7)

    float64_t Xn2, Xn3, Xn4, Xn5, Xn6, Xn7, Xn8;   /*  Input State variables     */
    float64_t Xn9, Xn10, Xn11, Xn12, Xn13, Xn14, Xn15, Xn16;
    float64_t acc2, acc3, acc4, acc5, acc6, acc7;  /*  Simulates the accumulator */
    float64_t acc8, acc9, acc10, acc11, acc12, acc13, acc14, acc15, acc16;

    do
    {
        /* Reading the coefficients */
        b0 = pCoeffs[0];
        b1 = pCoeffs[1];
        b2 = pCoeffs[2];
        a1 = pCoeffs[3];
        /* Apply loop unrolling and compute 16 output values simultaneously. */
        sample = blockSize >> 4u;
        a2 = pCoeffs[4];

        /*Reading the state values */
        d1 = pState[0];
        d2 = pState[1];

        pCoeffs += 5u;


        /* First part of the processing with loop unrolling.  Compute 16 outputs at a time.
         ** a second loop below computes the remaining 1 to 15 samples. */
        while(sample > 0u)
        {

            /* y[n] = b0 * x[n] + d1 */
            /* d1 = b1 * x[n] + a1 * y[n] + d2 */
            /* d2 = b2 * x[n] + a2 * y[n] */

            /* Read the first 2 inputs. 2 cycles */
            Xn1  = pIn[0 ];
            Xn2  = pIn[1 ];

            /* Sample 1. 5 cycles */
            Xn3  = pIn[2 ];
            acc1 = b0 * Xn1 + d1;

            Xn4  = pIn[3 ];
            d1 = b1 * Xn1 + d2;

            Xn5  = pIn[4 ];
            d2 = b2 * Xn1;

            Xn6  = pIn[5 ];
            d1 += a1 * acc1;

            Xn7  = pIn[6 ];
            d2 += a2 * acc1;

            /* Sample 2. 5 cycles */
            Xn8  = pIn[7 ];
            acc2 = b0 * Xn2 + d1;

            Xn9  = pIn[8 ];
            d1 = b1 * Xn2 + d2;

            Xn10 = pIn[9 ];
            d2 = b2 * Xn2;

            Xn11 = pIn[10];
            d1 += a1 * acc2;

            Xn12 = pIn[11];
            d2 += a2 * acc2;

            /* Sample 3. 5 cycles */
            Xn13 = pIn[12];
            acc3 = b0 * Xn3 + d1;

            Xn14 = pIn[13];
            d1 = b1 * Xn3 + d2;

            Xn15 = pIn[14];
            d2 = b2 * Xn3;

            Xn16 = pIn[15];
            d1 += a1 * acc3;

            pIn += 16;
            d2 += a2 * acc3;

            /* Sample 4. 5 cycles */
            acc4 = b0 * Xn4 + d1;
            d1 = b1 * Xn4 + d2;
            d2 = b2 * Xn4;
            d1 += a1 * acc4;
            d2 += a2 * acc4;

            /* Sample 5. 5 cycles */
            acc5 = b0 * Xn5 + d1;
            d1 = b1 * Xn5 + d2;
            d2 = b2 * Xn5;
            d1 += a1 * acc5;
            d2 += a2 * acc5;

            /* Sample 6. 5 cycles */
            acc6 = b0 * Xn6 + d1;
            d1 = b1 * Xn6 + d2;
            d2 = b2 * Xn6;
            d1 += a1 * acc6;
            d2 += a2 * acc6;

            /* Sample 7. 5 cycles */
            acc7 = b0 * Xn7 + d1;
            d1 = b1 * Xn7 + d2;
            d2 = b2 * Xn7;
            d1 += a1 * acc7;
            d2 += a2 * acc7;

            /* Sample 8. 5 cycles */
            acc8 = b0 * Xn8 + d1;
            d1 = b1 * Xn8 + d2;
            d2 = b2 * Xn8;
            d1 += a1 * acc8;
            d2 += a2 * acc8;

            /* Sample 9. 5 cycles */
            acc9 = b0 * Xn9 + d1;
            d1 = b1 * Xn9 + d2;
            d2 = b2 * Xn9;
            d1 += a1 * acc9;
            d2 += a2 * acc9;

            /* Sample 10. 5 cycles */
            acc10 = b0 * Xn10 + d1;
            d1 = b1 * Xn10 + d2;
            d2 = b2 * Xn10;
            d1 += a1 * acc10;
            d2 += a2 * acc10;

            /* Sample 11. 5 cycles */
            acc11 = b0 * Xn11 + d1;
            d1 = b1 * Xn11 + d2;
            d2 = b2 * Xn11;
            d1 += a1 * acc11;
            d2 += a2 * acc11;

            /* Sample 12. 5 cycles */
            acc12 = b0 * Xn12 + d1;
            d1 = b1 * Xn12 + d2;
            d2 = b2 * Xn12;
            d1 += a1 * acc12;
            d2 += a2 * acc12;

            /* Sample 13. 5 cycles */
            acc13 = b0 * Xn13 + d1;
            d1 = b1 * Xn13 + d2;
            d2 = b2 * Xn13;

            pOut[0 ] = acc1 ;
            d1 += a1 * acc13;

            pOut[1 ] = acc2 ;
            d2 += a2 * acc13;

            /* Sample 14. 5 cycles */
            pOut[2 ] = acc3 ;
            acc14 = b0 * Xn14 + d1;

            pOut[3 ] = acc4 ;
            d1 = b1 * Xn14 + d2;

            pOut[4 ] = acc5 ;
            d2 = b2 * Xn14;

            pOut[5 ] = acc6 ;
            d1 += a1 * acc14;

            pOut[6 ] = acc7 ;
            d2 += a2 * acc14;

            /* Sample 15. 5 cycles */
            pOut[7 ] = acc8 ;
            pOut[8 ] = acc9 ;
            acc15 = b0 * Xn15 + d1;

            pOut[9 ] = acc10;
            d1 = b1 * Xn15 + d2;

            pOut[10] = acc11;
            d2 = b2 * Xn15;

            pOut[11] = acc12;
            d1 += a1 * acc15;

            pOut[12] = acc13;
            d2 += a2 * acc15;

            /* Sample 16. 5 cycles */
            pOut[13] = acc14;
            acc16 = b0 * Xn16 + d1;

            pOut[14] = acc15;
            d1 = b1 * Xn16 + d2;

            pOut[15] = acc16;
            d2 = b2 * Xn16;

            sample--;
            d1 += a1 * acc16;

            pOut += 16;
            d2 += a2 * acc16;
        }

        sample = blockSize & 0xFu;
        while(sample > 0u)
        {
            Xn1 = *pIn;
            acc1 = b0 * Xn1 + d1;

            pIn++;
            d1 = b1 * Xn1 + d2;

            *pOut = acc1;
            d2 = b2 * Xn1;

            pOut++;
            d1 += a1 * acc1;

            sample--;
            d2 += a2 * acc1;
        }

        /* Store the updated state variables back into the state array */
        pState[0] = d1;
        /* The current stage input is given as the output to the next stage */
        pIn = pDst;

        pState[1] = d2;
        /* decrement the loop counter */
        stage--;

        pState += 2u;

        /*Reset the output working pointer */
        pOut = pDst;

    }
    while(stage > 0u);

#elif defined(ARM_MATH_CM0_FAMILY)

    /* Run the below code for Cortex-M0 */

    do
    {
        /* Reading the coefficients */
        b0 = *pCoeffs++;
        b1 = *pCoeffs++;
        b2 = *pCoeffs++;
        a1 = *pCoeffs++;
        a2 = *pCoeffs++;

        /*Reading the state values */
        d1 = pState[0];
        d2 = pState[1];


        sample = blockSize;

        while(sample > 0u)
        {
            /* Read the input */
            Xn1 = *pIn++;

            /* y[n] = b0 * x[n] + d1 */
            acc1 = (b0 * Xn1) + d1;

            /* Store the result in the accumulator in the destination buffer. */
            *pOut++ = acc1;

            /* Every time after the output is computed state should be updated. */
            /* d1 = b1 * x[n] + a1 * y[n] + d2 */
            d1 = ((b1 * Xn1) + (a1 * acc1)) + d2;

            /* d2 = b2 * x[n] + a2 * y[n] */
            d2 = (b2 * Xn1) + (a2 * acc1);

            /* decrement the loop counter */
            sample--;
        }

        /* Store the updated state variables back into the state array */
        *pState++ = d1;
        *pState++ = d2;

        /* The current stage input is given as the output to the next stage */
        pIn = pDst;

        /*Reset the output working pointer */
        pOut = pDst;

        /* decrement the loop counter */
        stage--;

    }
    while(stage > 0u);

#else

    float64_t Xn2, Xn3, Xn4;                  	  /*  Input State variables     */
    float64_t acc2, acc3, acc4;              		  /*  accumulator               */


    float64_t p0, p1, p2, p3, p4, A1;

    /* Run the below code for Cortex-M4 and Cortex-M3 */
    do
    {
        /* Reading the coefficients */
        b0 = *pCoeffs++;
        b1 = *pCoeffs++;
        b2 = *pCoeffs++;
        a1 = *pCoeffs++;
        a2 = *pCoeffs++;


        /*Reading the state values */
        d1 = pState[0];
        d2 = pState[1];

        /* Apply loop unrolling and compute 4 output values simultaneously. */
        sample = blockSize >> 2u;

        /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
        ** a second loop below computes the remaining 1 to 3 samples. */
        while(sample > 0u)
        {

            /* y[n] = b0 * x[n] + d1 */
            /* d1 = b1 * x[n] + a1 * y[n] + d2 */
            /* d2 = b2 * x[n] + a2 * y[n] */

            /* Read the four inputs */
            Xn1 = pIn[0];
            Xn2 = pIn[1];
            Xn3 = pIn[2];
            Xn4 = pIn[3];
            pIn += 4;

            p0 = b0 * Xn1;
            p1 = b1 * Xn1;
            acc1 = p0 + d1;
            p0 = b0 * Xn2;
            p3 = a1 * acc1;
            p2 = b2 * Xn1;
            A1 = p1 + p3;
            p4 = a2 * acc1;
            d1 = A1 + d2;
            d2 = p2 + p4;

            p1 = b1 * Xn2;
            acc2 = p0 + d1;
            p0 = b0 * Xn3;
            p3 = a1 * acc2;
            p2 = b2 * Xn2;
            A1 = p1 + p3;
            p4 = a2 * acc2;
            d1 = A1 + d2;
            d2 = p2 + p4;

            p1 = b1 * Xn3;
            acc3 = p0 + d1;
            p0 = b0 * Xn4;
            p3 = a1 * acc3;
            p2 = b2 * Xn3;
            A1 = p1 + p3;
            p4 = a2 * acc3;
            d1 = A1 + d2;
            d2 = p2 + p4;

            acc4 = p0 + d1;
            p1 = b1 * Xn4;
            p3 = a1 * acc4;
            p2 = b2 * Xn4;
            A1 = p1 + p3;
            p4 = a2 * acc4;
            d1 = A1 + d2;
            d2 = p2 + p4;

            pOut[0] = acc1;
            pOut[1] = acc2;
            pOut[2] = acc3;
            pOut[3] = acc4;
            pOut += 4;

            sample--;
        }

        sample = blockSize & 0x3u;
        while(sample > 0u)
        {
            Xn1 = *pIn++;

            p0 = b0 * Xn1;
            p1 = b1 * Xn1;
            acc1 = p0 + d1;
            p3 = a1 * acc1;
            p2 = b2 * Xn1;
            A1 = p1 + p3;
            p4 = a2 * acc1;
            d1 = A1 + d2;
            d2 = p2 + p4;

            *pOut++ = acc1;

            sample--;
        }

        /* Store the updated state variables back into the state array */
        *pState++ = d1;
        *pState++ = d2;

        /* The current stage input is given as the output to the next stage */
        pIn = pDst;

        /*Reset the output working pointer */
        pOut = pDst;

        /* decrement the loop counter */
        stage--;

    }
    while(stage > 0u);

#endif

}
LOW_OPTIMIZATION_EXIT

/**
   * @} end of BiquadCascadeDF2T group
   */
